The electron in a hydrogen atom makes a transition `n_1 rarr n_2` where `n_1 and n_2` are the principal quantum numbers of the two states. Assume the Bohr model to be valid. The time period of the electron in the initial state is eight times that in the final state. What are the possible values of `n_1 and n_2` ?

Explanation

The time period T of an electron in a Bohr orbit of principal quantum number n is:
`T=(2pin^3h^3)/(k^2mZ^2e^4)`
Thus `T alpha n^3`
`:. T_1/T_2 =n_1^3/n_2^3`
As `T_1 = 8T_2` , the above relation gives
`(n_1/n_2)^3= 8`
or `n_1 = 2n_2`
Thus the possible values of `n_1 and n_2` are
`n_1 = 2, n_2 = 1, n_1 = 4, n_2 = 2, n_1 =6, n_2 = 3`, and so on.....